Finding Regulatory Motifs in DNA Sequences - TIME.mk
Transcript of Finding Regulatory Motifs in DNA Sequences - TIME.mk
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Finding Regulatory Motifs in DNA Sequences
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Outline• Implanting Patterns in Random Text • Gene Regulation• Regulatory Motifs• The Gold Bug Problem• The Motif Finding Problem• Brute Force Motif Finding• The Median String Problem• Search Trees• Branch-and-Bound Motif Search• Branch-and-Bound Median String Search• Consensus and Pattern Branching: Greedy Motif Search• PMS: Exhaustive Motif Search
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Random Sample
atgaccgggatactgataccgtatttggcctaggcgtacacattagataaacgtatgaagtacgatgaccgggatactgataccgtatttggcctaggcgtacacattagataaacgtatgaagtacgatgaccgggatactgataccgtatttggcctaggcgtacacattagataaacgtatgaagtacgatgaccgggatactgataccgtatttggcctaggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgttagactcggcgccgccgttagactcggcgccgccgttagactcggcgccgccg
acccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaatactgggcataaggtacatactgggcataaggtacatactgggcataaggtacatactgggcataaggtaca
tgagtatccctgggatgacttttgggaacactatagtgctctcccgatttttgaatatgtaggatgagtatccctgggatgacttttgggaacactatagtgctctcccgatttttgaatatgtaggatgagtatccctgggatgacttttgggaacactatagtgctctcccgatttttgaatatgtaggatgagtatccctgggatgacttttgggaacactatagtgctctcccgatttttgaatatgtaggatcattcgccagggtccgatcattcgccagggtccgatcattcgccagggtccgatcattcgccagggtccga
gctgagaattggatgaccttgtaagtgttttccacgcaatcgcgaaccaacgcggacccaaagggctgagaattggatgaccttgtaagtgttttccacgcaatcgcgaaccaacgcggacccaaagggctgagaattggatgaccttgtaagtgttttccacgcaatcgcgaaccaacgcggacccaaagggctgagaattggatgaccttgtaagtgttttccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagacaagaccgataaaggagacaagaccgataaaggagacaagaccgataaaggaga
tcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatggcctcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatggcctcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatggcctcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatggcccacttagtccacttatagcacttagtccacttatagcacttagtccacttatagcacttagtccacttatag
gtcaatcatgttcttgtgaatggatttttaactgagggcatagaccgcttggcgcacccaaattgtcaatcatgttcttgtgaatggatttttaactgagggcatagaccgcttggcgcacccaaattgtcaatcatgttcttgtgaatggatttttaactgagggcatagaccgcttggcgcacccaaattgtcaatcatgttcttgtgaatggatttttaactgagggcatagaccgcttggcgcacccaaattcagtgtgggcgagcgcaacagtgtgggcgagcgcaacagtgtgggcgagcgcaacagtgtgggcgagcgcaa
cggttttggcccttgttagaggcccccgtactgatggaaactttcaattatgagagagctaatccggttttggcccttgttagaggcccccgtactgatggaaactttcaattatgagagagctaatccggttttggcccttgttagaggcccccgtactgatggaaactttcaattatgagagagctaatccggttttggcccttgttagaggcccccgtactgatggaaactttcaattatgagagagctaatctatcgcgtgcgtgttcattatcgcgtgcgtgttcattatcgcgtgcgtgttcattatcgcgtgcgtgttcat
aacttgagttggtttcgaaaatgctctggggcacatacaagaggagtcttccttatcagttaataacttgagttggtttcgaaaatgctctggggcacatacaagaggagtcttccttatcagttaataacttgagttggtttcgaaaatgctctggggcacatacaagaggagtcttccttatcagttaataacttgagttggtttcgaaaatgctctggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtagctgtatgacactatgtagctgtatgacactatgtagctgtatgacactatgta
ttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttcaacgtatttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttcaacgtatttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttcaacgtatttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttcaacgtatgccgaaccgaaagggaaggccgaaccgaaagggaaggccgaaccgaaagggaaggccgaaccgaaagggaag
ctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcttctgggtactgatagcattctgggtactgatagcattctgggtactgatagcattctgggtactgatagca
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Implanting Motif AAAAAAAGGGGGGGAAAAAAAGGGGGGGAAAAAAAGGGGGGGAAAAAAAGGGGGGG
atgaccgggatactgatatgaccgggatactgatatgaccgggatactgatatgaccgggatactgatAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccg
acccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaatatatataAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGaaaa
tgagtatccctgggatgactttgagtatccctgggatgactttgagtatccctgggatgactttgagtatccctgggatgacttAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGtgctctcccgatttttgaatatgtaggatcattcgccagggtccgatgctctcccgatttttgaatatgtaggatcattcgccagggtccgatgctctcccgatttttgaatatgtaggatcattcgccagggtccgatgctctcccgatttttgaatatgtaggatcattcgccagggtccga
gctgagaattggatggctgagaattggatggctgagaattggatggctgagaattggatgAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGtccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggaga
tcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaattcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaattcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaattcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGcttatagcttatagcttatagcttatag
gtcaatcatgttcttgtgaatggatttgtcaatcatgttcttgtgaatggatttgtcaatcatgttcttgtgaatggatttgtcaatcatgttcttgtgaatggatttAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGgaccgcttggcgcacccaaattcagtgtgggcgagcgcaagaccgcttggcgcacccaaattcagtgtgggcgagcgcaagaccgcttggcgcacccaaattcagtgtgggcgagcgcaagaccgcttggcgcacccaaattcagtgtgggcgagcgcaa
cggttttggcccttgttagaggcccccgtcggttttggcccttgttagaggcccccgtcggttttggcccttgttagaggcccccgtcggttttggcccttgttagaggcccccgtAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGcaattatgagagagctaatctatcgcgtgcgtgttcatcaattatgagagagctaatctatcgcgtgcgtgttcatcaattatgagagagctaatctatcgcgtgcgtgttcatcaattatgagagagctaatctatcgcgtgcgtgttcat
aacttgagttaacttgagttaacttgagttaacttgagttAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGctggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtactggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtactggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtactggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgta
ttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGaccgaaagggaagaccgaaagggaagaccgaaagggaagaccgaaagggaag
ctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcttttttttAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGAAAAAAAAGGGGGGGaaaa
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Where is the Implanted Motif?
atgaccgggatactgataaaaaaaagggggggggcgtacacattagataaacgtatgaagtacgatgaccgggatactgataaaaaaaagggggggggcgtacacattagataaacgtatgaagtacgatgaccgggatactgataaaaaaaagggggggggcgtacacattagataaacgtatgaagtacgatgaccgggatactgataaaaaaaagggggggggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgttagactcggcgccgccgttagactcggcgccgccgttagactcggcgccgccg
acccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaataaaaaaaaagggggggataaaaaaaaagggggggataaaaaaaaagggggggataaaaaaaaaggggggga
tgagtatccctgggatgacttaaaaaaaagggggggtgctctcccgatttttgaatatgtaggatgagtatccctgggatgacttaaaaaaaagggggggtgctctcccgatttttgaatatgtaggatgagtatccctgggatgacttaaaaaaaagggggggtgctctcccgatttttgaatatgtaggatgagtatccctgggatgacttaaaaaaaagggggggtgctctcccgatttttgaatatgtaggatcattcgccagggtccgatcattcgccagggtccgatcattcgccagggtccgatcattcgccagggtccga
gctgagaattggatgaaaaaaaagggggggtccacgcaatcgcgaaccaacgcggacccaaagggctgagaattggatgaaaaaaaagggggggtccacgcaatcgcgaaccaacgcggacccaaagggctgagaattggatgaaaaaaaagggggggtccacgcaatcgcgaaccaacgcggacccaaagggctgagaattggatgaaaaaaaagggggggtccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagacaagaccgataaaggagacaagaccgataaaggagacaagaccgataaaggaga
tcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaataaaatcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaataaaatcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaataaaatcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaataaaaaaaagggggggcttatagaaaagggggggcttatagaaaagggggggcttatagaaaagggggggcttatag
gtcaatcatgttcttgtgaatggatttaaaaaaaaggggggggaccgcttggcgcacccaaattgtcaatcatgttcttgtgaatggatttaaaaaaaaggggggggaccgcttggcgcacccaaattgtcaatcatgttcttgtgaatggatttaaaaaaaaggggggggaccgcttggcgcacccaaattgtcaatcatgttcttgtgaatggatttaaaaaaaaggggggggaccgcttggcgcacccaaattcagtgtgggcgagcgcaacagtgtgggcgagcgcaacagtgtgggcgagcgcaacagtgtgggcgagcgcaa
cggttttggcccttgttagaggcccccgtaaaaaaaagggggggcaattatgagagagctaatccggttttggcccttgttagaggcccccgtaaaaaaaagggggggcaattatgagagagctaatccggttttggcccttgttagaggcccccgtaaaaaaaagggggggcaattatgagagagctaatccggttttggcccttgttagaggcccccgtaaaaaaaagggggggcaattatgagagagctaatctatcgcgtgcgtgttcattatcgcgtgcgtgttcattatcgcgtgcgtgttcattatcgcgtgcgtgttcat
aacttgagttaaaaaaaagggggggctggggcacatacaagaggagtcttccttatcagttaataacttgagttaaaaaaaagggggggctggggcacatacaagaggagtcttccttatcagttaataacttgagttaaaaaaaagggggggctggggcacatacaagaggagtcttccttatcagttaataacttgagttaaaaaaaagggggggctggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtagctgtatgacactatgtagctgtatgacactatgtagctgtatgacactatgta
ttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcataaaaaaaaggttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcataaaaaaaaggttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcataaaaaaaaggttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcataaaaaaaagggggggaccgaaagggaaggggggaccgaaagggaaggggggaccgaaagggaaggggggaccgaaagggaag
ctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcttaaaaaaaagggggggattaaaaaaaagggggggattaaaaaaaagggggggattaaaaaaaaggggggga
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Implanting Motif AAAAAAGGGGGGG with Four Mutations
atgaccgggatactgatatgaccgggatactgatatgaccgggatactgatatgaccgggatactgatAAAAggggAAAAAAAAggggAAAGGAAAGGAAAGGAAAGGttttttttGGGGGGGGGGGGggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccg
acccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaatatatataccccAAAAAAAAttttAAAAAAAAAAAAAAAAccccGGGGGGGGccccGGGGGGGGGGGGaaaa
tgagtatccctgggatgactttgagtatccctgggatgactttgagtatccctgggatgactttgagtatccctgggatgacttAAAAAAAAAAAAAAAAttttAAAAAAAAttttGGGGGGGGaaaaGGGGttttGGGGGGGGtgctctcccgatttttgaatatgtaggatcattcgccagggtccgatgctctcccgatttttgaatatgtaggatcattcgccagggtccgatgctctcccgatttttgaatatgtaggatcattcgccagggtccgatgctctcccgatttttgaatatgtaggatcattcgccagggtccga
gctgagaattggatggctgagaattggatggctgagaattggatggctgagaattggatgccccAAAAAAAGGGAAAAAAAGGGAAAAAAAGGGAAAAAAAGGGattattattattGGGGtccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggaga
tcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaattcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaattcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaattcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatAAAAttttAAAAAAAAttttAAAGGAAAGGAAAGGAAAGGaaaaaaaaGGGGGGGGGGGGcttatagcttatagcttatagcttatag
gtcaatcatgttcttgtgaatggatttgtcaatcatgttcttgtgaatggatttgtcaatcatgttcttgtgaatggatttgtcaatcatgttcttgtgaatggatttAAAAAAAAccccAAAAAAAAttttAAGGGAAGGGAAGGGAAGGGctctctctGGGGGGGGgaccgcttggcgcacccaaattcagtgtgggcgagcgcaagaccgcttggcgcacccaaattcagtgtgggcgagcgcaagaccgcttggcgcacccaaattcagtgtgggcgagcgcaagaccgcttggcgcacccaaattcagtgtgggcgagcgcaa
cggttttggcccttgttagaggcccccgtcggttttggcccttgttagaggcccccgtcggttttggcccttgttagaggcccccgtcggttttggcccttgttagaggcccccgtAAAAttttAAAAAAAAAAAAccccAAGGAAGGAAGGAAGGaaaaGGGGGGGGGGGGcccccaattatgagagagctaatctatcgcgtgcgtgttcatcaattatgagagagctaatctatcgcgtgcgtgttcatcaattatgagagagctaatctatcgcgtgcgtgttcatcaattatgagagagctaatctatcgcgtgcgtgttcat
aacttgagttaacttgagttaacttgagttaacttgagttAAAAAAAAAAAAAAAAAAAAAAAAttttAGGGAGGGAGGGAGGGaaaaGGGGccccccccctggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtactggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtactggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtactggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgta
ttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatAAAActctctctAAAAAGGAAAAAGGAAAAAGGAAAAAGGaaaaGGGGccccGGGGGGGGaccgaaagggaagaccgaaagggaagaccgaaagggaagaccgaaagggaag
ctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcttttttttAAAActctctctAAAAAGGAAAAAGGAAAAAGGAAAAAGGaaaaGGGGccccGGGGGGGGaaaa
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Where is the Motif???
atgaccgggatactgatagaagaaaggttgggggcgtacacattagataaacgtatgaagtacgatgaccgggatactgatagaagaaaggttgggggcgtacacattagataaacgtatgaagtacgatgaccgggatactgatagaagaaaggttgggggcgtacacattagataaacgtatgaagtacgatgaccgggatactgatagaagaaaggttgggggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgttagactcggcgccgccgttagactcggcgccgccgttagactcggcgccgccg
acccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaatacaataaaacggcgggatacaataaaacggcgggatacaataaaacggcgggatacaataaaacggcggga
tgagtatccctgggatgacttaaaataatggagtggtgctctcccgatttttgaatatgtaggatgagtatccctgggatgacttaaaataatggagtggtgctctcccgatttttgaatatgtaggatgagtatccctgggatgacttaaaataatggagtggtgctctcccgatttttgaatatgtaggatgagtatccctgggatgacttaaaataatggagtggtgctctcccgatttttgaatatgtaggatcattcgccagggtccgatcattcgccagggtccgatcattcgccagggtccgatcattcgccagggtccga
gctgagaattggatgcaaaaaaagggattgtccacgcaatcgcgaaccaacgcggacccaaagggctgagaattggatgcaaaaaaagggattgtccacgcaatcgcgaaccaacgcggacccaaagggctgagaattggatgcaaaaaaagggattgtccacgcaatcgcgaaccaacgcggacccaaagggctgagaattggatgcaaaaaaagggattgtccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagacaagaccgataaaggagacaagaccgataaaggagacaagaccgataaaggaga
tcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatataatcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatataatcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatataatcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatataataaaggaagggcttatagtaaaggaagggcttatagtaaaggaagggcttatagtaaaggaagggcttatag
gtcaatcatgttcttgtgaatggatttaacaataagggctgggaccgcttggcgcacccaaattgtcaatcatgttcttgtgaatggatttaacaataagggctgggaccgcttggcgcacccaaattgtcaatcatgttcttgtgaatggatttaacaataagggctgggaccgcttggcgcacccaaattgtcaatcatgttcttgtgaatggatttaacaataagggctgggaccgcttggcgcacccaaattcagtgtgggcgagcgcaacagtgtgggcgagcgcaacagtgtgggcgagcgcaacagtgtgggcgagcgcaa
cggttttggcccttgttagaggcccccgtataaacaaggagggccaattatgagagagctaatccggttttggcccttgttagaggcccccgtataaacaaggagggccaattatgagagagctaatccggttttggcccttgttagaggcccccgtataaacaaggagggccaattatgagagagctaatccggttttggcccttgttagaggcccccgtataaacaaggagggccaattatgagagagctaatctatcgcgtgcgtgttcattatcgcgtgcgtgttcattatcgcgtgcgtgttcattatcgcgtgcgtgttcat
aacttgagttaaaaaatagggagccctggggcacatacaagaggagtcttccttatcagttaataacttgagttaaaaaatagggagccctggggcacatacaagaggagtcttccttatcagttaataacttgagttaaaaaatagggagccctggggcacatacaagaggagtcttccttatcagttaataacttgagttaaaaaatagggagccctggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtagctgtatgacactatgtagctgtatgacactatgtagctgtatgacactatgta
ttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatactaaaaaggttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatactaaaaaggttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatactaaaaaggttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatactaaaaaggagcggaccgaaagggaagagcggaccgaaagggaagagcggaccgaaagggaagagcggaccgaaagggaag
ctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcttactaaaaaggagcggattactaaaaaggagcggattactaaaaaggagcggattactaaaaaggagcgga
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Why Finding (15,4) Motif is Difficult?
atgaccgggatactgatatgaccgggatactgatatgaccgggatactgatatgaccgggatactgatAAAAggggAAAAAAAAggggAAAGGAAAGGAAAGGAAAGGttttttttGGGGGGGGGGGGggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccgggcgtacacattagataaacgtatgaagtacgttagactcggcgccgccg
acccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaaacccctattttttgagcagatttagtgacctggaaaaaaaatttgagtacaaaacttttccgaatatatataccccAAAAAAAAttttAAAAAAAAAAAAAAAAccccGGGGGGGGccccGGGGGGGGGGGGaaaa
tgagtatccctgggatgactttgagtatccctgggatgactttgagtatccctgggatgactttgagtatccctgggatgacttAAAAAAAAAAAAAAAAttttAAAAAAAAttttGGGGGGGGaaaaGGGGttttGGGGGGGGtgctctcccgatttttgaatatgtaggatcattcgccagggtccgatgctctcccgatttttgaatatgtaggatcattcgccagggtccgatgctctcccgatttttgaatatgtaggatcattcgccagggtccgatgctctcccgatttttgaatatgtaggatcattcgccagggtccga
gctgagaattggatggctgagaattggatggctgagaattggatggctgagaattggatgccccAAAAAAAGGGAAAAAAAGGGAAAAAAAGGGAAAAAAAGGGattattattattGGGGtccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggagatccacgcaatcgcgaaccaacgcggacccaaaggcaagaccgataaaggaga
tcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaattcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaattcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaattcccttttgcggtaatgtgccgggaggctggttacgtagggaagccctaacggacttaatAAAAttttAAAAAAAAttttAAAGGAAAGGAAAGGAAAGGaaaaaaaaGGGGGGGGGGGGcttatagcttatagcttatagcttatag
gtcaatcatgttcttgtgaatggatttgtcaatcatgttcttgtgaatggatttgtcaatcatgttcttgtgaatggatttgtcaatcatgttcttgtgaatggatttAAAAAAAAccccAAAAAAAAttttAAGGGAAGGGAAGGGAAGGGctctctctGGGGGGGGgaccgcttggcgcacccaaattcagtgtgggcgagcgcaagaccgcttggcgcacccaaattcagtgtgggcgagcgcaagaccgcttggcgcacccaaattcagtgtgggcgagcgcaagaccgcttggcgcacccaaattcagtgtgggcgagcgcaa
cggttttggcccttgttagaggcccccgtcggttttggcccttgttagaggcccccgtcggttttggcccttgttagaggcccccgtcggttttggcccttgttagaggcccccgtAAAAttttAAAAAAAAAAAAccccAAGGAAGGAAGGAAGGaaaaGGGGGGGGGGGGcccccaattatgagagagctaatctatcgcgtgcgtgttcatcaattatgagagagctaatctatcgcgtgcgtgttcatcaattatgagagagctaatctatcgcgtgcgtgttcatcaattatgagagagctaatctatcgcgtgcgtgttcat
aacttgagttaacttgagttaacttgagttaacttgagttAAAAAAAAAAAAAAAAAAAAAAAAttttAGGGAGGGAGGGAGGGaaaaGGGGccccccccctggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtactggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtactggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgtactggggcacatacaagaggagtcttccttatcagttaatgctgtatgacactatgta
ttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatttggcccattggctaaaagcccaacttgacaaatggaagatagaatccttgcatAAAActctctctAAAAAGGAAAAAGGAAAAAGGAAAAAGGaaaaGGGGccccGGGGGGGGaccgaaagggaagaccgaaagggaagaccgaaagggaagaccgaaagggaag
ctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcctggtgagcaacgacagattcttacgtgcattagctcgcttccggggatctaatagcacgaagcttttttttAAAActctctctAAAAAGGAAAAAGGAAAAAGGAAAAAGGaaaaGGGGccccGGGGGGGGaaaa
AAAAggggAAAAAAAAggggAAAGGAAAGGAAAGGAAAGGttttttttGGGGGGGGGGGG
ccccAAAAAAAAttttAAAAAAAAAAAAAAAAccccGGGGGGGGccccGGGGGGGGGGGG..|..|||.|..|||..|..|||.|..|||..|..|||.|..|||..|..|||.|..|||
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Challenge Problem
• Find a motif in a sample of - 20 “random” sequences (e.g. 600 nt long)- each sequence containing an implanted
pattern of length 15, - each pattern appearing with 4 mismatches
as (15,4)-motif.
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Combinatorial Gene Regulation
• A microarray experiment showed that when gene X is knocked out, 20 other genes are not expressed
• How can one gene have such drastic effects?
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Regulatory Proteins• Gene X encodes regulatory protein, a.k.a. a
transcription factor (TF)
• The 20 unexpressed genes rely on gene X’s TF to induce transcription
• A single TF may regulate multiple genes
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Regulatory Regions
• Every gene contains a regulatory region (RR) typically stretching 100-1000 bp upstream of the transcriptional start site
• Located within the RR are the Transcription Factor Binding Sites (TFBS), also known as motifs, specific for a given transcription factor
• TFs influence gene expression by binding to a specific location in the respective gene’s regulatory region -TFBS
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Transcription Factor Binding Sites
• A TFBS can be located anywhere within the Regulatory Region.
• TFBS may vary slightly across different regulatory regions since non-essential bases could mutate
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Motifs and Transcriptional Start Sites
geneATCCCG
geneTTCCGG
geneATCCCG
geneATGCCG
geneATGCCC
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Transcription Factors and Motifs
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Motif Logo
• Motifs can mutate on non important bases
• The five motifs in five different genes have mutations in position 3 and 5
• Representations called motif logos illustrate the conserved and variable regions of a motif
TGGGGGA
TGAGAGA
TGGGGGA
TGAGAGA
TGAGGGA
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Motif Logos: An Example
(http://www-lmmb.ncifcrf.gov/~toms/sequencelogo.html)
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Identifying Motifs
• Genes are turned on or off by regulatory proteins
• These proteins bind to upstream regulatory regions of genes to either attract or block an RNA polymerase
• Regulatory protein (TF) binds to a short DNA sequence called a motif (TFBS)
• So finding the same motif in multiple genes’regulatory regions suggests a regulatory relationship amongst those genes
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Identifying Motifs: Complications
• We do not know the motif sequence
• We do not know where it is located relative to the genes start
• Motifs can differ slightly from one gene to the next
• How to discern it from “random” motifs?
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
A Motif Finding Analogy
• The Motif Finding Problem is similar to the problem posed by Edgar Allan Poe (1809 – 1849) in his Gold Bug story
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Gold Bug Problem
• Given a secret message:53++!305))6*;4826)4+.)4+);806*;48!8`60))85;]8*:+*8!83(88)5
*!; 46(;88*96*?;8)*+(;485);5*!2:*+(;4956*2(5*-4)8`8*;
4069285);)6!8)4++;1(+9;48081;8:8+1;48!85;4)485!528806*81(+9;48;(88;4(
+?34;48)4+;161;:188;+?;
• Decipher the message encrypted in the fragment
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Hints for The Gold Bug Problem
• Additional hints:• The encrypted message is in English• Each symbol correspond to one letter in the
English alphabet• No punctuation marks are encoded
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Gold Bug Problem: Symbol Counts
• Naive approach to solving the problem:• Count the frequency of each symbol in the
encrypted message• Find the frequency of each letter in the
alphabet in the English language• Compare the frequencies of the previous
steps, try to find a correlation and map the symbols to a letter in the alphabet
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Symbol Frequencies in the Gold Bug Message
• Gold Bug Message:
• English Language:
e t a o i n s r h l d c u m f p g w y b v k x j q z
Most frequent Least frequent
Frequency
Symbol1
-2
`3
?11445567891112141516192534
.]:39201!(65*+)4;8
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Gold Bug Message Decoding: First Attempt
• By simply mapping the most frequent symbols to the most frequent letters of the alphabet:
sfiilfcsoorntaeuroaikoaiotecrntaeleyrcooestvenpinel efheeosnlt
arhteenmrnwteonihtaesotsnlupnihtamsrnuhsnbaoeyentac rmuesotorl
eoaiitdhimtaecedtepeidtaelestaoaeslsueecrnedhimtaet heetahiwfa
taeoaitdrdtpdeetiwt
• The result does not make sense
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Gold Bug Problem: l-tuple count
• A better approach:• Examine frequencies of l-tuples,
combinations of 2 symbols, 3 symbols, etc.• “The” is the most frequent 3-tuple in
English and “;48” is the most frequent 3-tuple in the encrypted text
• Make inferences of unknown symbols by examining other frequent l-tuples
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Gold Bug Problem: the ;48 clue
• Mapping “the” to “;48” and substituting all occurrences of the symbols:
53++!305))6* the 26)h+.)h+)te06* the !e`60))e5t]e*:+*e!e3(ee)5*!t
h6(tee*96*?te)*+( the 5)t5*!2:*+(th956*2(5*h)e`e*th0692e5)t)6!e
)h++t1(+9 the 0e1te:e+1 the !e5th)he5!52ee06*e1(+9 the t(eeth(+?3h t
he)h+t161t:1eet+?t
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Gold Bug Message Decoding: Second Attempt
• Make inferences:
53++!305))6*the26)h+.)h+)te06*the!e`60))e5t]e*:+*e! e3(ee)5*!t
h6(tee*96*?te)*+(the5)t5*!2:*+(th956*2(5*h)e`e*th06 92e5)t)6!e
)h++t1(+9the0e1te:e+1the!e5th)he5!52ee06*e1(+9 thet(ee th(+?3h t
he)h+t161t:1eet+?t
• “thet(ee” most likely means “the tree”• Infer “(“ = “r”
• “th(+?3h” becomes “thr+?3h”• Can we guess “+” and “?”?
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Gold Bug Problem: The Solution
• After figuring out all the mappings, the final message is:
AGOODGLASSINTHEBISHOPSHOSTELINTHEDEVILSSEATWENYONEDEGRE
ESANDTHIRTEENMINUTESNORTHEASTANDBYNORTHMAINBRANCHSEVENT HLIMBEASTSIDESHOOTFROMTHELEFTEYEOFTHEDEATHSHEADABEELINE
FROMTHETREETHROUGHTHESHOTFIFTYFEETOUT
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Solution (cont’d)
• Punctuation is important:
A GOOD GLASS IN THE BISHOP’S HOSTEL IN THE DEVIL’S SEA,
TWENY ONE DEGREES AND THIRTEEN MINUTES NORTHEAST AND BY NORTH,
MAIN BRANCH SEVENTH LIMB, EAST SIDE, SHOOT FROM THE LEFT EYE OF
THE DEATH’S HEAD A BEE LINE FROM THE TREE THROUGH T HE SHOT,
FIFTY FEET OUT.
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Solving the Gold Bug Problem
• Prerequisites to solve the problem:
• Need to know the relative frequencies of single letters, and combinations of two and three letters in English
• Knowledge of all the words in the English dictionary is highly desired to make accurate inferences
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
• Nucleotides in motifs encode for a message in the “genetic” language. Symbols in “The Gold Bug”encode for a message in English
• In order to solve the problem, we analyze the frequencies of patterns in DNA/Gold Bug message.
• Knowledge of established regulatory motifs makes the Motif Finding problem simpler. Knowledge of the words in the English dictionary helps to solve the Gold Bug problem.
Motif Finding and The Gold Bug Problem: Similarities
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Similarities (cont’d)
• Motif Finding:
• In order to solve the problem, we analyze the frequencies of patterns in the nucleotide sequences
• In order to solve the problem, we analyze the frequencies of patterns in the nucleotide sequences
• Gold Bug Problem:
• In order to solve the problem, we analyze the frequencies of patterns in the text written in English
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Similarities (cont’d)
• Motif Finding:• Knowledge of established motifs reduces
the complexity of the problem
• Gold Bug Problem:• Knowledge of the words in the dictionary is
highly desirable
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Motif Finding and The Gold Bug Problem: Differences
Motif Finding is harder than Gold Bug problem:
• We don’t have the complete dictionary of motifs• The “genetic” language does not have a
standard “grammar”• Only a small fraction of nucleotide sequences
encode for motifs; the size of data is enormous
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Motif Finding Problem
• Given a random sample of DNA sequences:
cctgatagacgctatctggctatccacgtacgtaggtcctctgtgcgaatctatgcgtttccaaccat
agtactggtgtacatttgatacgtacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc
aaacgtacgtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt
agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtacgtataca
ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaacgtacgtc
• Find the pattern that is implanted in each of the individual sequences, namely, the motif
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Motif Finding Problem (cont’d)
• Additional information:
• The hidden sequence is of length 8
• The pattern is not exactly the same in each array because random point mutations may occur in the sequences
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Motif Finding Problem (cont’d)
• The patterns revealed with no mutations:cctgatagacgctatctggctatccacgtacgtacgtacgtacgtacgtacgtacgtaggtcctctgtgcgaatctatgcgtttccaaccat
agtactggtgtacatttgatacgtacgtacgtacgtacgtacgtacgtacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc
aaacgtacgtacgtacgtacgtacgtacgtacgtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt
agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtacgtacgtacgtacgtacgtacgtacgtataca
ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaacgtacgtacgtacgtacgtacgtacgtacgtc
acgtacgtacgtacgtacgtacgtacgtacgt
Consensus String
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Motif Finding Problem (cont’d)
• The patterns with 2 point mutations:
cctgatagacgctatctggctatccaaaaGGGGgtacgtacgtacgtacTTTTttttaggtcctctgtgcgaatctatgcgtttccaaccat
agtactggtgtacatttgatCCCCccccAAAAtacgttacgttacgttacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc
aaacgtacgtacgtacgtTATATATAgtgtgtgtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt
agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtacgtacgtacgtCCCCccccAAAAttttataca
ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaCCCCcgtacgcgtacgcgtacgcgtacgGGGGc
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Motif Finding Problem (cont’d)
• The patterns with 2 point mutations:
cctgatagacgctatctggctatccaaaaGGGGgtacgtacgtacgtacTTTTttttaggtcctctgtgcgaatctatgcgtttccaaccat
agtactggtgtacatttgatCCCCccccAAAAtacgttacgttacgttacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc
aaacgtacgtacgtacgtTATATATAgtgtgtgtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacgaaaatttt
agcctccgatgtaagtcatagctgtaactattacctgccacccctattacatcttacgtacgtacgtacgtCCCCccccAAAAttttataca
ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctcgatcgttaCCCCcgtacgcgtacgcgtacgcgtacgGGGGc
Can we still find the motif, now that we have 2 mutations?
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Defining Motifs
• To define a motif, lets say we know where the motif starts in the sequence
• The motif start positions in their sequences can be represented as s = (s1,s2,s3,…,st)
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Motifs: Profiles and Consensusa a a a GGGG g t a c g t a c g t a c g t a c TTTT ttttCCCC c c c c AAAA t a c g tt a c g tt a c g tt a c g t
Alignment a c g t a c g t a c g t a c g t T AT AT AT A g tg tg tg ta c g t a c g t a c g t a c g t CCCC c c c c AAAA ttttCCCC c g t a c g c g t a c g c g t a c g c g t a c g GGGG
_________________
AAAA 3333 0 0 0 0 1111 0 0 0 0 3333 1 11 11 11 1 0000Profile CCCC 2222 4444 0 0 0 0 0 0 0 0 1111 4444 0 00 00 00 0
GGGG 0 1 0 1 0 1 0 1 4444 0 0 0 0 0 0 0 0 0 0 0 0 3333 1111TTTT 0 0 0 0 0 0 0 0 0 0 0 0 5555 1 0 1 0 1 0 1 0 1111 4444
_________________
Consensus A C G T A C G TA C G T A C G TA C G T A C G TA C G T A C G T
• Line up the patterns by their start indexes
s = (s1, s2, …, st)
• Construct matrix profile with frequencies of each nucleotide in columns
• Consensus nucleotide in each position has the highest score in column
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Consensus
• Think of consensus as an “ancestor” motif, from which mutated motifs emerged
• The distance between a real motif and the consensus sequence is generally less than that for two real motifs
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Consensus (cont’d)
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Evaluating Motifs
• We have a guess about the consensus sequence, but how “good” is this consensus?
• Need to introduce a scoring function to compare different guesses and choose the “best” one.
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Defining Some Terms
• t - number of sample DNA sequences• n - length of each DNA sequence• DNA - sample of DNA sequences (t x n array)
• llll - length of the motif (llll-mer)• si - starting position of an llll-mer in sequence i
• s=(s1, s2,… st) - array of motif’s starting positions
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Parameters
cctgatagacgctatctggctatcc aGgtacTtaggtcctctgtgcgaatctatgcgtttccaaccat
agtactggtgtacatttgat CcAtacgtacaccggcaacctgaaacaaacgctcagaaccagaagtgc
aaacgtTAgtgcaccctctttcttcgtggctctggccaacgagggctgatgtataagacga aaatttt
agcctccgatgtaagtcatagctgtaactattacctgccacccctattaca tctt acgtCcAtataca
ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctc gatcgtta CcgtacgGc
l = 8
t=5
s1= 26 s2= 21 s3= 3 s4= 56 s5= 60s
DNA
n = 69
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Scoring Motifs
• Given s = (s1, … st) and DNA:
Score(s,DNA) =
a G g t a c T tC c A t a c g ta c g t T A g ta c g t C c A tC c g t a c g G
_________________
A 3 0 1 0 3 1 1 0C 2 4 0 0 1 4 0 0G 0 1 4 0 0 0 3 1T 0 0 0 5 1 0 1 4
_________________
Consensus a c g t a c g t
Score 3+4+4+5+3+4+3+4=30
l
t
∑= ∈
l
i GCTAk
ikcount1 },,,{
),(max
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Motif Finding Problem
• If starting positions s=(s1, s2,… st) are given, finding consensus is easy even with mutations in the sequences because we can simply construct the profile to find the motif (consensus)
• But… the starting positions s are usually not given. How can we find the “best” profile matrix?
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Motif Finding Problem: Formulation
• Goal: Given a set of DNA sequences, find a set of llll-mers, one from each sequence, that maximizes the consensus score
• Input: A t x n matrix of DNA, and llll, the length of the pattern to find
• Output: An array of t starting positions s = (s1, s2, … st) maximizing Score(s,DNA)
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Motif Finding Problem: Brute Force Solution
• Compute the scores for each possible combination of starting positions s
• The best score will determine the best profile and the consensus pattern in DNA
• The goal is to maximize Score(s,DNA) by varying the starting positions si, where:
si = [1, …, nnnn-llll+1]
iiii = [1, …, tttt]
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
BruteForceMotifSearch
1. BruteForceMotifSearch(DNADNADNADNA, tttt, nnnn, llll)
2.2.2.2. bestScorebestScorebestScorebestScore � 0
3.3.3.3. forforforfor each s=s=s=s=(s1,s2 , . . ., st) from (1,1 . . . 1) to (nnnn-llll+1, . . ., nnnn-llll+1)
4. ifififif (Score(ssss,DNADNADNADNA) > bestScorebestScorebestScorebestScore)
5. bestScorebestScorebestScorebestScore � score(s, s, s, s, DNADNADNADNA)
6. bestMotifbestMotifbestMotifbestMotif � (s1,s2 , . . . , st)
7.7.7.7. returnreturnreturnreturn bestMotifbestMotifbestMotifbestMotif
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Running Time of BruteForceMotifSearch
• Varying (n - llll + 1) positions in each of tsequences, we’re looking at (n - llll + 1)t sets of starting positions
• For each set of starting positions, the scoring function makes llll operations, so complexity is l l l l (n – llll + 1)t = O(llll nt)
• That means that for t = 8, n = 1000, llll = 10 we must perform approximately 1020 computations – it will take billions years
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Median String Problem
• Given a set of t DNA sequences find a pattern that appears in all t sequences with the minimum number of mutations
• This pattern will be the motif
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Hamming Distance
• Hamming distance:• dH(v,w) is the number of nucleotide pairs
that do not match when v and w are aligned. For example:
dH(AAAAAA,ACAAAC) = 2
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Total Distance: An Example
• Given v = “acgtacgt” and s
acgtacgt
cctgatagacgctatctggctatcc acgtacgt aggtcctctgtgcgaatctatgcgtttccaaccatacgtacgt
agtactggtgtacatttgat acgtacgt acaccggcaacctgaaacaaacgctcagaaccagaagtgcacgtacgt
aaacgtacgt gcaccctctttcttcgtggctctggccaacgagggctgatgtataagacga aaattttacgtacgt
agcctccgatgtaagtcatagctgtaactattacctgccacccctattaca tctt acgtacgt atacaacgtacgt
ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctc gatcgtta acgtacgt c
v is the sequence in red, x is the sequence in blue
• TotalDistance(vvvv,DNADNADNADNA) = 0
dH(v, x) = 0
dH(v, x) = 0
dH(v, x) = 0 dH(v, x) = 0
dH(v, x) = 0
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Total Distance: Example
• Given v = “acgtacgt” and s
acgtac gtcctgatagacgctatctggctatcc acgtac At aggtcctctgtgcgaatctatgcgtttccaaccat
acgtacgtagtactggtgtacatttgat acgtacgt acaccggcaacctgaaacaaacgctcagaaccagaagtgc
acgt acgt
aaaAgt Ccgt gcaccctctttcttcgtggctctggccaacgagggctgatgtataagacga aaattttacgtacgt
agcctccgatgtaagtcatagctgtaactattacctgccacccctattaca tctt acgtacgt atacaacgta cgt
ctgttatacaacgcgtcatggcggggtatgcgttttggtcgtcgtacgctc gatcgtta acgta Ggt c
v is the sequence in red, x is the sequence in blue
• TotalDistance(vvvv,DNADNADNADNA) = 1+0+2+0+1 = 4
dH(v, x) = 2
dH(v, x) = 1
dH(v, x) = 0
dH(v, x) = 0
dH(v, x) = 1
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Total Distance: Definition
• For each DNA sequence i, compute all dH(v, x), where x is an llll- merwith starting position si
(1 < si < n – l l l l + 1)• Find minimum of dH(v, x) among all llll- mers in
sequence i• TotalDistance(v,DNA) is the sum of the minimum
Hamming distances for each DNA sequence i• TotalDistance(v,DNA) = mins dH(v, s), where s is
the set of starting positions s1, s2,… st
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
The Median String Problem: Formulation
• Goal: Given a set of DNA sequences, find a median string
• Input: A t x n matrix DNA, and llll, the length of the pattern to find
• Output: A string v of llll nucleotides that minimizes TotalDistance(v,DNA) over all strings of that length
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Median String Search Algorithm
1. MedianStringSearch (DNA, t, n, llll)
2. bestWord � AAA…A3. bestDistance � ∞
4. for each llll-mer s from AAA…A to TTT…Tif TotalDistance(s,DNA) < bestDistance
5. bestDistance�TotalDistance(s,DNA)6. bestWord � s7. return bestWord
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Motif Finding Problem == Median String Problem
• The Motif Finding is a maximization problem while Median String is a minimization problem
• However, the Motif Finding problem and Median String problem are computationally equivalent
• Need to show that minimizing TotalDistanceis equivalent to maximizing Score
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
We are looking for the same thing
a G g t a c T tC c A t a c g t
Alignment a c g t T A g ta c g t C c A tC c g t a c g G
_________________
A 3 0 1 0 3 1 1 0Profile C 2 4 0 0 1 4 0 0
G 0 1 4 0 0 0 3 1 T 0 0 0 5 1 0 1 4
_________________
Consensus a c g t a c g t
Score 3+4+4+5+3+4+3+4
TotalDistance 2+1+1+0+2+1+2+1
Sum 5 5 5 5 5 5 5 5
• At any column iScorei+ TotalDistancei = tttt
• Because there are llll columnsScore + TotalDistance = llll * tttt
• Rearranging:Score= llll * tttt - TotalDistance
• llll * t is constant the minimization of the right side is equivalent to the maximization of the left side
l
t
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Motif Finding Problem vs. Median String Problem• Why bother reformulating the Motif Finding
problem into the Median String problem?
• The Motif Finding Problem needs to examine all the combinations for s. That is (n - llll + 1)t combinations!!!
• The Median String Problem needs to examine all 4llll combinations for v. This number is relatively smaller
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Motif Finding: Improving the Running Time
Recall the BruteForceMotifSearch:
1. BruteForceMotifSearch(DNADNADNADNA, tttt, nnnn, llll)
2. bestScorebestScorebestScorebestScore � 0
3. forforforfor each s=s=s=s=(s1,s2 , . . ., st) from (1,1 . . . 1) to (nnnn-llll+1, . . ., nnnn-llll+1)
4. ifififif (Score(ssss,DNADNADNADNA) > bestScorebestScorebestScorebestScore)
5. bestScorebestScorebestScorebestScore � Score(ssss, , , , DNADNADNADNA)
6. bestMotifbestMotifbestMotifbestMotif � (s1,s2 , . . . , st)
7. return bestMotifbestMotifbestMotifbestMotif
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Structuring the Search
• How can we perform the line
forforforfor each s=s=s=s=(s1,s2 , . . ., st) from (1,1 . . . 1) to (nnnn-llll+1, . . ., nnnn-llll+1) ?
• We need a method for efficiently structuring and navigating the many possible motifs
• This is not very different than exploring all t-digit numbers
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Median String: Improving the Running Time
1. MedianStringSearch (DNA, t, n, llll)
2. bestWord � AAA…A3. bestDistance � ∞
4. for each llll-mer s from AAA…A to TTT…Tif TotalDistance(s,DNA) < bestDistance
5. bestDistance�TotalDistance(s,DNA)6. bestWord � s7. return bestWord
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Structuring the Search
• For the Median String Problem we need to consider all 4llll possible llll-mers:
aa… aa
aa… ac
aa… ag
aa… at
.
.
tt… tt
How to organize this search?
llll
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Alternative Representation of the Search Space
• Let A = 1, C = 2, G = 3, T = 4• Then the sequences from AA…A to TT…T become:
11…1111…1211…1311…14
.
.44…44
• Notice that the sequences above simply list all numbers as if we were counting on base 4 without using 0 as a digit
llll
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Linked List
• Suppose llll = 2
aa ac ag at ca cc cg ct ga gc gg gt ta tc tg tt
• Need to visit all the predecessors of a sequence before visiting the sequence itself
Start
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Linked List (cont’d)
• Linked list is not the most efficient data structure for motif finding
• Let’s try grouping the sequences by their prefixes
aa ac ag at ca cc cg ct ga gc gg gt ta tc tg tt
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Search Tree
a- c- g- t-
aa ac ag at ca cc cg ct ga gc gg gt ta tc tg tt
--
root
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Analyzing Search Trees
• Characteristics of the search trees:• The sequences are contained in its leaves• The parent of a node is the prefix of its
children• How can we move through the tree?
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Moving through the Search Trees
• Four common moves in a search tree that we are about to explore:• Move to the next leaf• Visit all the leaves• Visit the next node• Bypass the children of a node
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Visit the Next Leaf
1. NextLeaf( aaaa,L, k k k k ) // a a a a : the array of digits2.2.2.2. forforforfor iiii � L to 1 // L: length of the array3. ifififif ai < kkkk // kkkk : max digit value4. ai � ai + 15. returnreturnreturnreturn aaaa6. ai � 17.7.7.7. returnreturnreturnreturn aaaa
Given a current leaf a , we need to compute the “next” leaf:
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
NextLeaf (cont’d)
• The algorithm is common addition in radix k:
• Increment the least significant digit
• “Carry the one” to the next digit position when the digit is at maximal value
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
NextLeaf: Example
• Moving to the next leaf:
1- 2- 3- 4-
11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44
--Current Location
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
NextLeaf: Example (cont’d)
• Moving to the next leaf:
1- 2- 3- 4-
11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44
--Next Location
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Visit All Leaves
• Printing all permutations in ascending order:
1. AllLeaves(L,kkkk) // L: length of the sequence
2. aaaa � (1,...,1) // kkkk : max digit value
3.3.3.3. whilewhilewhilewhile forever // aaaa :::: array of digits
4. output aaaa
5. aaaa � NextLeaf(aaaa,L,kkkk)
6. ifififif aaaa = (1,...,1)
7. returnreturnreturnreturn
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Visit All Leaves: Example
• Moving through all the leaves in order:
1- 2- 3- 4-
11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
--
Order of steps
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Depth First Search
• So we can search leaves
• How about searching all vertices of the tree?
• We can do this with a depth first search
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Visit the Next Vertex1. NextVertex(aaaa,iiii,L,kkkk) // aaaa : the array of digits2. ifififif iiii < L // iiii : prefix length3. a i+1 � 1 // L: max length4. returnreturnreturnreturn ( aaaa,iiii+1) // kkkk : max digit value5. elseelseelseelse6. forforforfor jjjj � llll to 17. ifififif aj < kkkk8. aj � aj +19. returnreturnreturnreturn( aaaa,j j j j )10. returnreturnreturnreturn(aaaa,0)
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Example
• Moving to the next vertex:
1- 2- 3- 4-
11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44
--Current Location
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Example
• Moving to the next vertices:
1- 2- 3- 4-
11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44
--
Location after 5 next vertex moves
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Bypass Move
• Given a prefix (internal vertex), find next vertex after skipping all its children
1. Bypass(aaaa,iiii,L,kkkk) // aaaa: array of digits
2. forforforfor jjjj � i to 1 // iiii : prefix length
3. ifififif aj < kkkk // L: maximum length
4. aj � aj +1 // kkkk : max digit value
5. returnreturnreturnreturn(aaaa,jjjj)
6. returnreturnreturnreturn(aaaa,0)
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Bypass Move: Example
• Bypassing the descendants of “2-”:
1- 2- 3- 4-
11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44
--Current Location
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Example
• Bypassing the descendants of “2-”:
1- 2- 3- 4-
11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44
--Next Location
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Revisiting Brute Force Search
• Now that we have method for navigating the tree, lets look again at BruteForceMotifSearch
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Brute Force Search Again
1. BruteForceMotifSearchAgain(DNADNADNADNA, tttt, nnnn, llll)
2. s s s s � (1,1,…, 1)
3. bestScorebestScorebestScorebestScore � Score(s,DNADNADNADNA)
4. whilewhilewhilewhile forever
5. ssss � NextLeaf (ssss, tttt, nnnn- llll +1)
6. ifififif (Score(ssss,DNADNADNADNA) > bestScorebestScorebestScorebestScore)
7. bestScorebestScorebestScorebestScore � Scorecorecorecore(ssss, , , , DNADNADNADNA)
8. bestMotifbestMotifbestMotifbestMotif � (s1,s2 , . . . , st)
9. returnreturnreturnreturn bestMotifbestMotifbestMotifbestMotif
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Can We Do Better?
• Sets of s=(s1, s2, …,st) may have a weak profile for the first i positions (s1, s2, …,si)
• Every row of alignment may add at most llll to Score• Optimism: if all subsequent (t-i) positions (si+1, …st)
add (tttt – i i i i ) * llll to Score(ssss,iiii,DNADNADNADNA)
• If Score(s,i,DNA) + (t – iiii ) * llll < BestScoreBestScoreBestScoreBestScore, it makes no sense to search in vertices of the current subtree• Use ByPass()
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Branch and Bound Algorithm for Motif Search
• Since each level of the tree goes deeper into search, discarding a prefix discards all following branches
• This saves us from looking at (n – llll + 1)t-i leaves• Use NextVertex() and
ByPass() to navigate the tree
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Pseudocode for Branch and Bound Motif Search
1. BranchAndBoundMotifSearch(DNA,t,n,llll)2. s � (1,…,1)3. bestScore � 04. i � 15. while i > 06. if i < t7. optimisticScore � Score(s, i, DNA) +(t – i ) * llll8. if optimisticScore < bestScore9. (s, i) � Bypass(s,i, n-l l l l +1)10. else 11. (s, i) � NextVertex(s, i, n-llll +1)12. else 13. if Score(s,DNA) > bestScore14. bestScore � Score(s)15. bestMotif � (s1, s2, s3, …, st)16. (s,i) � NextVertex(s,i,t,n-llll + 1)17. return bestMotif
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Median String Search Improvements
• Recall the computational differences between motif search and median string search
• The Motif Finding Problem needs to examine all (n-llll +1)t combinations for s.
• The Median String Problem needs to examine 4llll
combinations of v. This number is relatively small
• We want to use median string algorithm with the Branch and Bound trick!
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Branch and Bound Applied to Median String Search
• Note that if the total distance for a prefix is greater than that for the best word so far:
TotalDistance (prefixprefixprefixprefix, DNADNADNADNA) > BestDistanceBestDistanceBestDistanceBestDistance
there is no use exploring the remaining part of the word
• We can eliminate that branch and BYPASS exploring that branch further
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Bounded Median String Search1. BranchAndBoundMedianStringSearch(DNADNADNADNA,tttt,nnnn,llll )2.2.2.2. ssss � (1,…,1)3.3.3.3. bestDistancebestDistancebestDistancebestDistance � ∞
4. iiii � 15.5.5.5. whilewhilewhilewhile iiii > 06.6.6.6. ifififif iiii < llll7. prefixprefixprefixprefix � string corresponding to the first i nucleotides of ssss8. optimisticDistanceoptimisticDistanceoptimisticDistanceoptimisticDistance � TotalDistance(prefixprefixprefixprefix,DNADNADNADNA)9. ifififif optimisticDistanceoptimisticDistanceoptimisticDistanceoptimisticDistance > bestDistancebestDistancebestDistancebestDistance10. (ssss, i i i i ) � Bypass(ssss,iiii, llll, 4)11. elseelseelseelse12. (ssss, iiii ) � NextVertex(s,s,s,s, iiii, llll, 4)13. else else else else 14. wordwordwordword � nucleotide string corresponding to ssss15. if if if if TotalDistance(ssss,DNADNADNADNA) < bestDistancebestDistancebestDistancebestDistance16. bestDistancebestDistancebestDistancebestDistance � TotalDistance(wordwordwordword, DNADNADNADNA)17. bestWordbestWordbestWordbestWord � wordwordwordword18. (ssss,i i i i ) � NextVertex(ssss,iiii,llll, 4)19.19.19.19. return return return return bestWordbestWordbestWordbestWord
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Improving the Bounds
• Given an llll-mer w, divided into two parts at point i• u : prefix w1, …, wi, • v : suffix wi+1, ..., wllll
• Find minimum distance for u in a sequence
• No instances of u in the sequence have distance less than the minimum distance
• Note this doesn’t tell us anything about whether u is part of any motif. We only get a minimum distance for prefix u
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Improving the Bounds (cont’d)
• Repeating the process for the suffix v gives us a minimum distance for v
• Since u and v are two substrings of w, and included in motif w, we can assume that the minimum distance of u plus minimum distance of v can only be less than the minimum distance for w
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Better Bounds
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Better Bounds (cont’d)
• If d(prefix) + d(suffix) > bestDistance:
• Motif w (prefix.suffix) cannot give a better (lower) score than d(prefix) + d(suffix)
• In this case, we can ByPass()
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Better Bounded Median String Search1. ImprovedBranchAndBoundMedianString(DNA,t,n,llll)2. s = (1, 1, …, 1)3. bestdistance = ∞4. i = 15. while i > 06. if i < llll7. prefix = nucleotide string corresponding to (s1, s2, s3, …, si )8. optimisticPrefixDistance = TotalDistance (prefix, DNA)9. if (optimisticPrefixDistance < bestsubstring[ i ])10. bestsubstring[ i ] = optimisticPrefixDistance11. if (llll - i < i )12. optimisticSufxDistance = bestsubstring[llll -i ] 13. else14. optimisticSufxDistance = 0;15. if optimisticPrefixDistance + optimisticSufxDistance > bestDistance16. (s, i ) = Bypass(s, i, llll, 4)17. else18. (s, i ) = NextVertex(s, i, llll,4)19. else20. word = nucleotide string corresponding to (s1,s2, s3, …, st)21. if TotalDistance( word, DNA) < bestDistance22. bestDistance = TotalDistance(word, DNA)23. bestWord = word24. (s,i) = NextVertex(s, i,llll, 4)25. return bestWord
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
More on the Motif Problem
• Exhaustive Search and Median String are both exact algorithms
• They always find the optimal solution, though they may be too slow to perform practical tasks
• Many algorithms sacrifice optimal solution for speed
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
CONSENSUS: Greedy Motif Search
• Find two closest l-mers in sequences 1 and 2 and forms 2 x l alignment matrix with Score(s,2,DNA)
• At each of the following t-2 iterations CONSENSUS finds a “best”l-mer in sequence i from the perspective of the already constructed (i-1) x l alignment matrix for the first (i-1) sequences
• In other words, it finds an l-mer in sequence i maximizing
Score(s,i,DNA)
under the assumption that the first (i-1) l-mers have been already chosen
• CONSENSUS sacrifices optimal solution for speed: in fact the bulk of the time is actually spent locating the first 2 l-mers
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Some Motif Finding Programs
• CONSENSUSHertz, Stromo (1989)
• GibbsDNALawrence et al (1993)
• MEMEBailey, Elkan (1995)
• RandomProjectionsBuhler, Tompa (2002)
• MULTIPROFILER Keich, Pevzner (2002)
• MITRAEskin, Pevzner (2002)
• Pattern BranchingPrice, Pevzner (2003)
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Planted Motif Challenge
• Input:• n sequences of length m each.
• Output: • Motif M, of length l• Variants of interest have a hamming distance of d
from M
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
How to proceed?
• Exhaustive search?
• Run time is high
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
How to search motif space?
Start from random sample strings
Search motif space for the star
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Search small neighborhoods
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Exhaustive local search
A lot of work, most of it unecessary
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Best Neighbor
Branch from the seed strings
Find best neighbor -highest score
Don’t consider branches where the upper bound is not as good as best score so far
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Scoring
• PatternBranching use total distance score:• For each sequence Si in the sample S = {S1, . . . , Sn}, let
d(A, Si) = min{d(A, P) | P ∈ Si}.• Then the total distance of A from the sample is
d(A, S) = ∑ Si ∈ S d(A, Si).
• For a pattern A, let D=Neighbor(A) be the set of patterns which differ from A in exactly 1 position.
• We define BestNeighbor(A) as the pattern B ∈ D=Neighbor(A) with lowest total distance d(B, S).
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
PatternBranching Algorithm
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
PatternBranching Performance
• PatternBranching is faster than other pattern-based algorithms
• Motif Challenge Problem: • sample of n = 20 sequences• N = 600 nucleotides long• implanted pattern of length l = 15 • k = 4 mutations
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
PMS (Planted Motif Search)
• Generate all possible l-mers from out of the input sequence Si. Let Ci be the collection of these l-mers.
• Example:AAGTCAGGAGTCi = 3-mers:AAG AGT GTC TCA CAG AGG GGA GAG AGT
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
All patterns at Hamming distance d = 1
AAG AGT GTC TCA CAG AGG GGA GAG AGTCAG CGT ATC ACA AAG CGG AGA AAG CGTGAG GGT CTC CCA GAG TGG CGA CAG GGTTAG TGT TTC GCA TAG GGG TGA TAG TGTACG ACT GAC TAA CCG ACG GAA GCG ACTAGG ATT GCC TGA CGG ATG GCA GGG ATTATG AAT GGC TTA CTG AAG GTA GTG AATAAC AGA GTA TCC CAA AGA GGC GAA AGAAAA AGC GTG TCG CAC AGT GGG GAC AGCAAT AGG GTT TCT CAT AGC GGT GAT AGG
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Sort the lists
AAG AGT GTC TCA CAG AGG GGA GAG AGTAAA AAT ATC ACA AAG AAG AGA AAG AAT
AAC ACT CTC CCA CAA ACG CGA CAG ACTAAT AGA GAC GCA CAC AGA GAA GAA AGA
ACG AGC GCC TAA CAT AGC GCA GAC AGC
AGG AGG GGC TCC CCG AGT GGC GAT AGGATG ATT GTA TCG CGG ATG GGG GCG ATT
CAG CGT GTG TCT CTG CGG GGT GGG CGT
GAG GGT GTT TGA GAG GGG GTA GTG GGTTAG TGT TTC TTA TAG TGG TGA TAG TGT
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Eliminate duplicates
AAG AGT GTC TCA CAG AGG GGA GAG AGTAAA AAT ATC ACA AAG AAG AGA AAG AATAAC ACT CTC CCA CAA ACG CGA CAG ACTAAT AGA GAC GCA CAC AGA GAA GAA AGAACG AGC GCC TAA CAT AGC GCA GAC AGCAGG AGG GGC TCC CCG AGT GGC GAT AGGATG ATT GTA TCG CGG ATG GGG GCG ATTCAG CGT GTG TCT CTG CGG GGT GGG CGTGAG GGT GTT TGA GAG GGG GTA GTG GGTTAG TGT TTC TTA TAG TGG TGA TAG TGT
http://www.time.mk/trajkovski/teaching/eurm/bio.htmlTrajkovski: Motifs in DNA sequences
Find motif common to all lists
• Follow this procedure for all sequences• Find the motif common all Li (once duplicates
have been eliminated)• This is the planted motif